Mutual-visibility and general position in double graphs and in Mycielskians

The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles

Haplotype-resolved genome assembly of the tetraploid potato cultivar Désirée

Cultivar Désirée is an important model for potato functional genomics studies to assist breeding strategies. Here, we present a haplotype-resolved genome assembly of Désirée, achieved by assembling PacBio HiFi reads and Hi-C scaffolding, resulting in a high-contiguity chromosome-level assembly. We implemented a comprehensive annotation pipeline incorporating gene models and functional annotations from the Solanum tuberosum Phureja DM reference genome alongside RNA-seq reads to provide high-quality gene and transcript annotations. Additionally, we provide a genome-wide DNA methylation profile using Oxford Nanopore reads, enabling insights into potato epigenetics. The assembled genome, annotations, methylation and expression data are visualised in a publicly accessible genome browser (https://desiree.nib.si), providing a valuable resource for the potato research community